In such a known tool (EP 1 698 432 A2) for the fine-machining of optically active surfaces, in particular on spectacle lenses, a spherical head is arranged at the end of the guide element and engages in an associated receiving chamber of the machining disk, so that the machining disk can tilt relative to the guide element at the spherical head. If, for example, a higher relative machining speed is desired in order to increase the removal of material, the tool must be brought into engagement with the workpiece in the edge region, i.e. at a radial distance from the tool rotation axis. In this case, a return movement of the machining disk relative to the workpiece in the direction of the tool rotation axis may be obtained by tilting the machining disk at the spherical head. This may result in relative positions between the machining disk and the workpiece in which an undefinable removal of material on the workpiece is obtained, which is undesirable in applications in precision optics. In the known tool, the rotating drive of the machining disk takes place by means of an elastic bellows, which is fixed on the one hand to the main body and on the other hand to the machining disk by ring clips.
What is needed is a tool of the type specified in the introduction, which allows a stable, clearly definable polishing and/or fine-grinding process for applications in precision optics.